SOLUTION: What is the coefficient of x^2 in (x^3 + x^2 + x + 1)(5x^7 - 3x^4 + 10x^2 - 15)?

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Question 1209342: What is the coefficient of x^2 in (x^3 + x^2 + x + 1)(5x^7 - 3x^4 + 10x^2 - 15)?
Found 3 solutions by mccravyedwin, math_tutor2020, greenestamps:
Answer by mccravyedwin(407)   (Show Source): You can put this solution on YOUR website!

(x3 + x2 + x + 1)(5x7 - 3x4 + 10x2 - 15)

We'll get a term in x2 when we 

A. multiply the term x2 in the expression on the left by the term
-15 in the expression on the right, getting -15x2.

and when we

B. multiply the term 1 in the expression on the left by the 10x2 in
the expression on the right, getting 10x2

That's -15x2 + 10x2 = -5x2, 

And the coefficient is --- 

     tada! ---

           -5

Edwin
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Let,
f(x) = x^3 + x^2 + x + 1
g(x) = 5x^7 - 3x^4 + 10x^2 - 15

The goal is to find the x^2 coefficient in f(x)*g(x)

I'll use the box method

Place the terms of f(x) along the top.
Place the terms of g(x) along the left side.
x^3x^2x1
5x^7
-3x^4
10x^2
-15


To fill out this table, we multiply the headers.
For instance 5x^10 would go in the top left corner (because x^3 times 5x^7 = 5x^10).
But since 5x^10 isn't an x^2 term, we'll leave this cell blank.

We only fill the cells that have x^2 in them
x^3x^2x1
5x^7
-3x^4
10x^210x^2
-15-15x^2

That would be -15x^2 and 10x^2
They combine to -5x^2

Answer: -5
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!




The partial products that contribute to the x^2 term in the product come from multiplying....

(1) the x^2 term in the first polynomial and the constant term in the second: (x^2)(-15) = -15x^2
(2) the x term in the first polynomial and the x term in the second: (x)(0x) = 0x^2
(1) the constant term in the first polynomial and the x^2 term in the second: (1)(10x^2) = 10x^2

(-15x^2) + (0x^2) + (10x^2) = -5x^2

ANSWER: the coefficient of x^2 in the product is -5
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